Chapter 12: Q. 11 (page 816)

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{t_{n}\} = \{\frac{1}{2} - \frac{1}{3} n\}$

Short Answer

Expert verified

The solution is $d = - \frac{1}{3}$ ; first four terms $= \frac{1}{6}, - \frac{1}{6}, - \frac{1}{2}, - \frac{5}{6}$ .

Step by step solution

Step 1. Given information

$\{t_{n}\} = \{\frac{1}{2} - \frac{1}{3} n\}$

Step 2. Calculation

The first term is $t_{1} = \frac{1}{2} - \frac{1}{3} \cdot 1 = \frac{1}{6}$ .

The $n$ th term and the $(n - 1)$ st term of the sequence are-

$t_{n} = \frac{1}{2} - \frac{1}{3} n$ and $t_{n - 1} = \frac{1}{2} - \frac{1}{3} (n - 1) = \frac{1}{2} - \frac{1}{3} n + \frac{1}{3} = \frac{5}{6} - \frac{1}{3} n$

The common difference is -

$d = t_{n} - t_{n - 1} = (\frac{1}{2} - \frac{1}{3} n) - (\frac{5}{6} - \frac{1}{3} n) = - \frac{1}{3}$

Since the difference of any two successive terms is the constant $- \frac{1}{3}$ , the sequence $\{t_{n}\}$ is arithmetic.

The first four terms are $\frac{1}{6}, - \frac{1}{6}, - \frac{1}{2}, - \frac{5}{6}$ .

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In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{t_{n}\} = \{\frac{1}{2} - \frac{1}{3} n\}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.tn=12-13n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{t_{n}\} = \{\frac{1}{2} - \frac{1}{3} n\}$